Jenkinson is enjoying a run in the Arsenal starting lineup in the absence of Bacary Sagna, with the Gunners yet to concede this season in two goalless draws.
He said that Arsenal are more than capable of picking up the three points away to Liverpool on Sunday, September 2.
The 20-year-old told the club's official website: "It would be a huge statement of intent to win there. Anfield is always a great place to play football, we're all looking forward to it and we're going for the three points.
"Liverpool are a big club but we are just focused on our own game, and hopefully we will execute as we need to and get the three points."
Arsene Wenger's side have a good recent record against Liverpool, and have not lost at Anfield in four seasons.